Dirac equation in curved spacetime

In mathematical physics, the Dirac equation in curved spacetime is a generalization of the Dirac equation from flat spacetime (Minkowski space) to curved spacetime, a general Lorentzian manifold. == Mathematical formulation == === Spacetime === In full generality the equation can be defined on M {\displaystyle M} or ( M , g ) {\displaystyle (M,\mathbf {g} )} a pseudo-Riemannian manifold, but for concreteness we restrict to pseudo-Riemannian manifold with signature ( − + + + ) {\displaystyle (-+++)} .

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